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Tau vs PI

My opinion on this is that it's a simple guage transformation that is useful in spherical trig or calculating compound angles but that's it.
Math is a tool. An elaborate extension to describe whatever we choose to measure.

PI is a reasonably accurate description of the ratio of diameter to circumference.
Tau is a reasonable accurate description of the ratio of radius to circumference.

"When measuring angles, mathematicians don't use degrees, they use radians," Houston enthusiastically told Life's Little Mysteries, a sister site to LiveScience. "There are 2pi radians in a circle. This means one quarter of a circle corresponds to half of pi. That is, one quarter corresponds to a half. That's crazy. Similarly, three quarters of a circle is three halves of pi. Three quarters corresponds to three halves!" [A Real Pie Chart: America's Favorite Pies]

"Let's now use tau," he continued. "One quarter of a circle is one quarter of tau. One quarter corresponds to one quarter! Isn't that sensible and easy to remember? Similarly, three quarters of a circle is three quarters of tau." Making tau equal to the full angular turn through a circle, he said, is "so easy and would prevent math, physics and engineering students from making silly errors."

Looking back on learning calculus and other angular math subjects, 1tau around the circle would have made a lot more sense than 2pi.

Although, once you understand the concept behind it all, it doesn't matter if you're using 1tau, 2pi, or 8.42girtles. As long as everyone is clear and remains clear about what the different symbols mean and how they apply to the math and concepts.

On another note, it kind of just depends where you want to apply the 2:

C = 2 * pi * r OR
C = tau * r OR
C = pi * d OR
C = tau * (1/2) * d

It kind of just depends on what number you want to use, r or d, and based on that, pi or tau.